[Paper Review] An Axiomatic Approach to General Intelligence: SANC(E3) -- Self-organizing Active Network of Concepts with Energy E3

Daesuk Kwon, Won-Gi Paeng|arXiv (Cornell University)|Jan 13, 2026

Embodied and Extended Cognition0 citations

TL;DR

The paper introduces SANC(𝐄₃), an axiomatic framework where representational units (Gestalts) emerge under finite capacity by minimizing an energy E₃ that balances reconstruction, structure, and update costs; it unifies perception, imagination, planning, and action through Gestalt completion and pseudo-memory-mapped I/O.

ABSTRACT

General intelligence must reorganize experience into internal structures that enable prediction and action under finite resources. Existing systems implicitly presuppose fixed primitive units -- tokens, subwords, pixels, or predefined sensor channels -- thereby bypassing the question of how representational units themselves emerge and stabilize. This paper proposes SANC(E3), an axiomatic framework in which representational units are not given a priori but instead arise as stable outcomes of competitive selection, reconstruction, and compression under finite activation capacity, governed by the explicit minimization of an energy functional E3. SANC(E3) draws a principled distinction between system tokens -- structural anchors such as {here, now, I} and sensory sources -- and tokens that emerge through self-organization during co-occurring events. Five core axioms formalize finite capacity, association from co-occurrence, similarity-based competition, confidence-based stabilization, and the reconstruction-compression-update trade-off. A key feature is a pseudo-memory-mapped I/O mechanism, through which internally replayed Gestalts are processed via the same axiomatic pathway as external sensory input. As a result, perception, imagination, prediction, planning, and action are unified within a single representational and energetic process. From the axioms, twelve propositions are derived, showing that category formation, hierarchical organization, unsupervised learning, and high-level cognitive activities can all be understood as instances of Gestalt completion under E3 minimization.

Motivation & Objective

• Define general intelligence via axioms where tokens are emergent rather than given a priori.
• Formalize a finite-capacity, energy-minimizing system (E₃) that governs token emergence and stabilization.
• Derive mechanisms for Gestalt formation, categorization, hierarchy, and unsupervised learning from first principles.
• Unify perception, imagination, prediction, planning, and action under a single representational process.

Proposed method

• Propose E₃ = λ₁L_rec + λ₂C_struct + λ₃C_update as the core objective for intelligent dynamics.
• Introduce Axioms A1–A5 to constrain capacity, competition, association, stabilization, and co-occurrence-driven candidates.
• Define tokens, system tokens, Gestalts, and the co-occurrence/association mechanics that generate representations (D1–D6).
• Establish mechanism axioms A6–A10 for closure under composition, hierarchical self-organization, cross-level isomorphism, and inter-subsystem communication.
• Derive twelve propositions (T1–T12) showing how categorization, hierarchy, unsupervised learning, and high-level cognition arise from Gestalt completion under E₃.
• Present a pseudo-memory-mapped I/O loop where replayed Gestalts follow the same axioms as external input.

Experimental results

Research questions

• RQ1 What minimal axioms must a system satisfy to exhibit general intelligence under finite resources?
• RQ2 How do emergent representational units (Gestalts) form and stabilize without predefined tokens?
• RQ3 How does the E₃ objective balance reconstruction, structure, and update to prevent token explosion or stagnation?
• RQ4 Can perception, imagination, prediction, planning, and action be unified under Gestalt completion?
• RQ5 How do hierarchical and self-similar structures arise from the axioms and dynamics?

Key findings

• Tokens other than system tokens are not exempt from competition or extinction (except pre-defined system tokens).
• Under finite capacity, turnover of Gestalts is inevitable due to competition and limited activation.
• All tokens except system tokens are generated as emergent stabilized structures optimizing E₃.
• A balanced E₃ prevents token and sequence explosions, yielding a stable repertoire.
• Category formation arises as compression that lowers both reconstruction error and structural complexity.
• Prediction manifests as Gestalt completion through partial-match retrieval and internal replay, aligning with Gestalt principles.
• Hierarchy and self-similar organization emerge from closure and level-homogeneous dynamics, enabling multi-level processing.
• System tokens (anchors) are relational and their meaning evolves relationally as context changes.